Tom Johnston

Improved bounds for 1-independent percolation on $\mathbb{Z}^n$

A 1-independent bond percolation model on a graph $G$ is a probability distribution on the spanning subgraphs of $G$ in which the states of the edges in vertex disjoint subgraphs are independent. These occur naturally when renormalising independent percolation models, but there is still relatively little known about them. We will give some improved bounds on one of the most well-studied cases, $\mathbb{Z}^n$.